Upvote:4
According to the visitor in transit visa page:
Documents you need
To apply for a Visitor in Transit visa, you must have a current passport or other valid travel identification document.
You need to provide evidence that you’re allowed to enter the country you’re travelling to, such as a:
- residence permit
- green card
- valid visa
If you’re not a resident or national of the country you’re travelling to, you may need to explain why you’re going there. You may need to provide details of where you’re staying.
You must also provide evidence that your onward journey is booked or confirmed, such as:
- a flight booking email
- printed tickets
- confirmation from a travel agent
(...)
(emphasis mine)
So you do indeed need to apply for the Schengen visa first, and once you have that you will be able to apply for the UK Visitor in Transit visa.